This article studies a hyperbolic conservation law that models
a highly re-entrant manufacturing system as encountered in
semi-conductor production.
Characteristic features are the nonlocal character of the velocity
and that the influx and outflux constitute the control and output
signal, respectively.
We prove the existence and uniqueness of solutions for $L^1$-data,
and study their regularity properties.
We also prove the existence of optimal controls
that minimizes in the $L^2$-sense the mismatch between the actual
and a desired output signal.
Finally, the time-optimal control for a step between equilibrium states is
identified and proven to be optimal.